Mathematics – Rings and Algebras
Scientific paper
2007-06-13
Israel J. Math. 171 (2009), no. 1, 1-14
Mathematics
Rings and Algebras
10 pages. This version has been revised according to a referee's suggestions. The additions include a discussion of the (lower
Scientific paper
10.1007/s11856-009-0036-7
A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to show the abundance of elements of N_p. Our main result shows that any divisor n of q-1, where q is a power of p, such that $n\ge (p-1)^{1/p} (q-1)^{1-1/(2p)}$, belongs to N_p. This extends its special case for p=2 which was proved in a previous paper by a different method.
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